Protocols for password-based authenticated key exchange (PAKE) allow two users who share only a short, low-entropy password to agree on a cryptographically strong session key. One must ensure that protocols are immune to off-line dictionary attacks in which an adversary exhaustively enumerates all possible passwords in an attempt to determine the correct one. Recently Katz, et al. [6] gave a new framework for realizing PAKE without random oracles, in the common reference string model. In this paper, we instantiate the framework of [6] under the lattices assumptions. Specifically, we modified the lattice-based approximate projective hashing introduced in [11] and plug it into the framework of [6], and we prove our new PAKE is efficient and secure based on the security of GK's PAKE framework [6] in the standard model.